A cyclist achieves optimal pedaling efficiency when there is little to no wasted force exerted on a pedal. This occurs when force is exerted on the pedal in a direction tangential to the arc of pedal travel in the direction of rotation of the cycle's crank. Forces exerted by the cyclist in any other direction are considered wasted forces, which reduce the cyclist's efficiency. By actively analyzing their pedaling strokes, cyclists may be able to correct their motion to minimize the amount of wasted forces produced, and thus increase their efficiency and endurance.
Previous devices and systems have been developed to analyze forces applied by a cyclist on a pedal. Such previous devices and systems have used strain gauges or piezoresistors mounted on a pedal, on other parts of a cycle, or on the shoes or cleats of the cyclist. The previous devices and systems, however, have required extensive calibration and complicated equipment, and therefore have been limited to use in the laboratory.
One such system is described in Reiser II, et al., “Instrumented bicycle pedals for dynamic measurement of propulsive cycling loads,” Sports Engineering, 2003, vol. 6, pp. 41-48 (“the Reiser system”). The sensor arrangement of the Reiser system is illustrated in FIG. 1. As shown in FIG. 1, the sensor arrangement includes eight strain gauges 1021-1028 affixed to an outer surface of a pedal spindle 104, which is coupled to a crank arm 106 of a bicycle. In operation, the eight strain gauges 1021-1028 are wired to form two complete Wheatstone bridge arrangements such that each bridge measures an applied force component either normal or tangential to the surface of the pedal. This configuration allows the force to be measured independently of the location due to the fact that the applied force is proportional to a difference in a measured deformation, or strain, at each row of strain gauges 1021-1028. Thus, a moment Mi at a first bridge of gauges 1021-1024 or a second bridge of gauges 1025-1028 due to an applied force F, at a distance x from the second bridge of gauges 1025-1028 is equal to Mi=F·x, and the moment at a distance x+L from the first bridge of gauges 1021-1024 is equal to Mm=F·(x+L). Using these equations for the moments, the force F can be given as
  F  =                              M          m                -                  M          i                    L        .  
The moments at the first bridge of gauges 1021-1024 and at the second bridge of gauges 1025-1028 are related to the surface strains εm and εi, respectively, measured by the bridges, and respectively given by:
                              M          m                =                              ɛ            m                    ·          I          ·          E                    c        ⁢                  ⁢    and    ⁢                  ⁢                            M          i                =                              ɛ            i                    ·          I          ·          E                    c        ,wherein I is the moment of inertia, E is the Young's Modulus, and c is a maximum distance from a neutral surface. Using the above equations, the force F can be determined from the surface strains measured by each of the bridges, while being independent of the location of the applied force such that
  F  =                    I        ·        E            c        ·                  (                                            ɛ              m                        -                          ɛ              i                                L                )            .      
Accordingly, the Reiser system provides a compact pedal-spindle-mounted sensor system that allows for the measurement of forces applied by a cyclist on a pedal. The data obtained by strain gauges 1021-1028 is transmitted through a cable connected to the pedal spindle to an external computer for the determination of the applied forces.
But, the Reiser system requires the use of a modified pedal, the enlargement of the threaded pedal spindle hole of the crank, and a specially machined pedal spindle having the sensors attached thereto. The Reiser system is also only accurate using specially designed pedal spindles which, unlike standard commercially-available pedal spindles, are designed and built to have a linear response to applied forces. Moreover, the Reiser system also requires complex external electronics, including a portable computer, in order to provide data, thus making the system impractical for immediate analysis by a cyclist while riding.
In addition, there have been other systems and devices which have been designed to measure forces applied by a cyclist on a pedal, including modified pedals having sensors built into the pedals, and sensors to be placed on or in a cyclist's shoe or cleat. The prior art pedals, however, often require extensive external electronics for processing, making them unsuitable for use outside of a laboratory. In addition, those systems and devices that have been designed for portability often require specialized equipment, are susceptible to damage from external environmental factors, or produce results which are very noisy, and thus are unable to provide accurate, useful results to the cyclist.